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Full text of "Mathematical And Physical Papers - Iii"

ON THE MOTION OF PENDULUMS.                        13
When simplified in the manner just explained, the equations such as (1) become
dp __    f cPu     d*u     d*u \ ^   du^
dp =    fd*v      d^     d*v\       fo dy~~ ^ \dxz     dy*      dz2 J    P dt
dp ___    /d*w     d*w    d*w\       dw which, with the equation of continuity,"
_____i            I________A                                               /Q\
~~~i       i" ~~7~~   "i       T     ~~" >/ * \ v/
ax    dy     dz
are the only equations which have to be satisfied at all points of the fluid, and at all instants of time.
In applying equations (2) to a particular pendulum experiment, we may suppose p constant; but in order to compare experiments made in summer with experiments made in winter, or experiments made under a high barometer with experiments made under a low, it will be requisite to regard p, as a quantity which may vary with the temperature and pressure of the fluid. As far as the result of a single experiment*, which has been already mentioned, performed with a single elastic fluid, namely air, justifies us in drawing such a general conclusion, we may assert that for a given fluid at a given temperature p varies as pf.
2. For the formation of the equations such as (1), I must refer to my former paper; but it will be possible, in a few words, to enable the reader to form a clear idea of the meaning of the constant p.
Conceive the fluid to move in planes parallel to the plane of   . ocy, the motion taking place in a direction parallel to the axis of y. The motion will evidently consist of a sort of continuous sliding, and the differential coefficient dv/dz may be taken as a measure of
* The first of the experiments described in Col. Sabine's paper, in which the gauge stood as high as 7 inches, leads to the same conclusion; but as the vacuum apparatus had not yet been made stanch it is perhaps hardly safe to trust this experiment in a question of such delicacy.
t [We now know that ^ is independent of p, until excessive exhaustions are reached, far beyond any that we have here to deal with.]
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